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Submission #367654

# Submission time Handle Problem Language Result Execution time Memory
367654 2021-02-17T21:54:33 Z 534351 Aesthetic (NOI20_aesthetic) C++17
13 / 100
 2000 ms 83536 KB 
#include <bits/stdc++.h>

using namespace std;

template<class T, class U>
void ckmin(T &a, U b)
{
    if (a > b) a = b;
}

template<class T, class U>
void ckmax(T &a, U b)
{
    if (a < b) a = b;
}

#define MP make_pair
#define PB push_back
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define SZ(x) ((int) (x).size())
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, a, b) for (auto i = (a); i < (b); i++)
#define FORD(i, a, b) for (auto i = (a) - 1; i >= (b); i--)

const int MAXN = 3e5 + 13;
const long long LLINF = 3e18;

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
typedef pair<pll, int> ppi;

int N, M, C, T;
vector<ppi> edge[MAXN];
ll dist[2][MAXN];
ll D;
int st[MAXN], ft[MAXN];
bitset<MAXN> seen;
vi bcc[MAXN];
int parent[MAXN];
vpi edges;

void dijkstra(int u)
{
    bool b = (u > 0);
    fill(dist[b], dist[b] + N + 1, LLINF);
    dist[b][u] = 0;
    priority_queue<pll, vector<pll>, greater<pll> > pq;
    pq.push({0, u});
    while(!pq.empty())
    {
        ll d = pq.top().fi; int u = pq.top().se; pq.pop();
        if (d != dist[b][u]) continue;
        for (auto e : edge[u])
        {
            int v = e.se; ll nd = d + e.fi.fi;
            if (nd < dist[b][v])
            {
                dist[b][v] = nd;
                pq.push({nd, v});
            }
        }
    }
}

void dfs(int u, int p)
{
	st[u] = T;
	ft[u] = T;
	T++;
	seen[u] = true;
	for (auto e : edge[u])
	{
        int v = e.se; ll d = e.fi.fi;
        if (dist[0][u] + d + dist[1][v] >= D && dist[1][u] + d + dist[0][v] >= D) continue;
        //oh no it is part of a path shorter than D, so the edge actually exists.
		if (v == p) continue;
		if (seen[v])
		{
			if (st[v] > st[u]) continue;
			edges.PB({u, v});
			ckmin(ft[u], st[v]);
			continue;
		}
        // cerr << u << ' ' << v << endl;
        // cerr << (bool) (dist[0][u] + d + dist[1][v] < D) << ' ' << (bool) (dist[1][u] + d + dist[0][v] < D) << endl;
		edges.PB({u, v});
        parent[v] = u;
		dfs(v, u);
		ckmin(ft[u], ft[v]);
		if (ft[v] >= st[u])
		{
			while(!edges.empty())
			{
				pii p = edges.back();
				edges.pop_back();
				bcc[C].PB(p.fi);
				bcc[C].PB(p.se);
				if (p == MP(u, v)) break;
			}
			C++;
		}
	}
}

bool check()
{
    //can you make the dist >D?
    //ans is YES if there's a bridge & this thing extends dist by more than D.
    T = 0;
    fill(st, st + N, 0);
    fill(ft, ft + N, 0);
    seen.reset();
    FOR(i, 0, C) bcc[i].clear();
    C = 0;
    FOR(i, 0, N)
    {
        if (seen[i]) continue;
        if (i == N - 1) return false;
        dfs(i, N);
    }
    set<pii> blocks;
    for (int i = N - 1; i != 0; i = parent[i])
    {
        blocks.insert({i, parent[i]});
        blocks.insert({parent[i], i});
    }
    set<pii> bridges;
    FOR(i, 0, C)
    {
        sort(ALL(bcc[i]));
        bcc[i].erase(unique(ALL(bcc[i])), bcc[i].end());
        if (SZ(bcc[i]) == 2)
        {
            bridges.insert({bcc[i][0], bcc[i][1]});
            bridges.insert({bcc[i][1], bcc[i][0]});
        }
    }
    FOR(u, 0, N)
    {
        for (auto e : edge[u])
        {
            int v = e.se; ll mx = e.fi.se;
            if (bridges.find({u, v}) == bridges.end()) continue;
            if (blocks.find({u, v}) == blocks.end()) continue;
            // cerr << u << ' ' << v << ' ' << mx << ' ' << dist[0][u] + mx + dist[1][v] << ' ' << dist[1][u] + mx + dist[0][v] << endl;
            if (dist[0][u] + mx + dist[1][v] >= D && dist[1][u] + mx + dist[0][v] >= D) return true;
        }
    }
    return false;
    //now just check if there's something we can extend that is a bridge.
}

int32_t main()
{
    cout << fixed << setprecision(12);
    cerr << fixed << setprecision(4);
    ios_base::sync_with_stdio(false); cin.tie(0);
    cin >> N >> M;
    vector<array<int, 3> > eds;
    FOR(i, 0, M)
    {
        int a, b, w;
        cin >> a >> b >> w; a--; b--;
        if (a == b) continue;
        eds.PB({a, b, w});
    }
    reverse(ALL(eds));
    int mx = 0;
    for (auto e : eds)
    {
        int a = e[0], b = e[1], w = e[2];
        edge[a].PB({{w, w + mx}, b});
        edge[b].PB({{w, w + mx}, a});
        ckmax(mx, w);
    }
    dijkstra(0);
    dijkstra(N - 1);
    ll lo = dist[0][N - 1], hi = LLINF;
    // cerr << mx << ' '<< lo << ' ' << hi << endl;
    while(hi > lo)
    {
        D = (hi + lo + 1) >> 1;
        if (check()) lo = D;
        else hi = D - 1;
    }
    cout << lo << '\n';
    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 14444 KB Output is correct
2 Correct 11 ms 14508 KB Output is correct
3 Correct 11 ms 14572 KB Output is correct
4 Correct 11 ms 14444 KB Output is correct
5 Correct 11 ms 14592 KB Output is correct
6 Correct 11 ms 14572 KB Output is correct
7 Correct 11 ms 14572 KB Output is correct
8 Correct 11 ms 14572 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 14444 KB Output is correct
2 Correct 11 ms 14508 KB Output is correct
3 Correct 11 ms 14572 KB Output is correct
4 Correct 11 ms 14444 KB Output is correct
5 Correct 11 ms 14592 KB Output is correct
6 Correct 11 ms 14572 KB Output is correct
7 Correct 11 ms 14572 KB Output is correct
8 Correct 11 ms 14572 KB Output is correct
9 Correct 36 ms 14956 KB Output is correct
10 Correct 39 ms 14956 KB Output is correct
11 Correct 27 ms 14828 KB Output is correct
12 Correct 27 ms 14848 KB Output is correct
13 Correct 24 ms 14828 KB Output is correct
14 Correct 25 ms 14828 KB Output is correct
15 Correct 24 ms 14844 KB Output is correct
16 Correct 24 ms 14956 KB Output is correct

Subtask #3
0 / 7.0

# Verdict Execution time Memory Grader output
1 Execution timed out 2090 ms 82000 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #4
0 / 15.0

# Verdict Execution time Memory Grader output
1 Execution timed out 2089 ms 83536 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #5
0 / 16.0

# Verdict Execution time Memory Grader output
1 Execution timed out 2086 ms 68772 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #6
0 / 22.0

# Verdict Execution time Memory Grader output
1 Execution timed out 2086 ms 68772 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #7
0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 14444 KB Output is correct
2 Correct 11 ms 14508 KB Output is correct
3 Correct 11 ms 14572 KB Output is correct
4 Correct 11 ms 14444 KB Output is correct
5 Correct 11 ms 14592 KB Output is correct
6 Correct 11 ms 14572 KB Output is correct
7 Correct 11 ms 14572 KB Output is correct
8 Correct 11 ms 14572 KB Output is correct
9 Correct 36 ms 14956 KB Output is correct
10 Correct 39 ms 14956 KB Output is correct
11 Correct 27 ms 14828 KB Output is correct
12 Correct 27 ms 14848 KB Output is correct
13 Correct 24 ms 14828 KB Output is correct
14 Correct 25 ms 14828 KB Output is correct
15 Correct 24 ms 14844 KB Output is correct
16 Correct 24 ms 14956 KB Output is correct
17 Execution timed out 2090 ms 82000 KB Time limit exceeded
18 Halted 0 ms 0 KB -